Bike race problem

Question

In a bicycle race, Lionel gives Robert 500 m advantage. Also, Lionel agrees to start 15 min after Robert. If Lionel bikes at 17 km/h and Robert at 14 km/h, how long will it take Lionel after he starts biking to overtake Robert?

Answer 1

Let's call:

 

v : speed of Robert

d : distance traveled by Robert

t : time from Robert's start

 

v = d / t  which is equivalent to d (m) = v * t = 14*10³/60 (m/min) * t (min)

 

The distance traveled by Lionel is d+500.

The time for Lionel is t-15, because he starts 15 min after Robert.

Thus Lionel's equation is: d+500 (m) = 17 * 10³/60 (m/min) * (t-15) (min)

 

You now have 2 equation with 2 unknowns:

 

d = 14*10³/60 * t

d + 500 = 17 * 10³/60 * (t-15)

 

You substitute the first equation in the second equation:

 

 14*10³/60 * t + 500 = 17*10³/60 * (t-15)

 50*t = 3750

 t = 75 min

 

So Lionel's time is t - 15 = 60 min